Magnetized effects of double diffusion model on mixed convective Casson nanofluid subject to generalized perspective of Fourier and Fick’s laws

Understanding the flow behavior of non-Newtonian fluids from an industrial standpoint is crucial. Many industrial and technical activities, such as the extrusion of polymer sheets, the manufacturing of paper, and the development of photographic films, require non-Newtonian fluids. Heat and mass transport have various manufacturing uses. However, classical heat and mass transfer theories (Fourier and Fick laws) cannot anticipate thermal and solute relaxation time occurrences. The purpose of this investigation is to apply the modified Ohm law to the heat and mass transportation systems, which are established by generalized Fourier and Fick’s equations, respectively. A three-dimensional Darcy–Forchheimer flow through a porous medium integrating Hall and ion slip effects is studied for a non-Newtonian fluid known as a “Casson nanofluid” with mixed convection across a stretched surface. To investigate heat transfer augmentation, the modified Buongiorno model for nanofluids is used. It covers practical nanofluid properties as well as the mechanics of random motion and thermo-migration in nanoparticles. These groups of Partial Differential Equations (PDEs) that represent the mathematical model are combined with the proper similarity transformations to create an ordinary differential equations system, which is then resolved using the power of the Lobatto IIIA method. Examples of numerical and graphical data are given to show how various physical constraints affect the variation for velocities, temperatures, mass transfer, dimensionless shear stress, as well as Nusselt and Sherwood numbers. It turns out that lowering the Casson fluid parameters’ values reduces the velocity in the spatial coordinates (x, y). A rise in the Hall parameter's values ultimately leads to an improvement in the fluid. This paper sheds light on useful applications including power generation, conservation of energy, friction elimination, and nanofluidics. Nonetheless, the work highlights an important point: by carefully adjusting the Casson parameter, thermophoresis parameter, and Brownian motion parameter, the flow of a Casson fluid, including nanoparticles, may be controlled.